Modeling Leukemia in Children Using Phase-type Distribution

Background: In this study, with the aim of modeling Leukemia in children using Phase-type distribution, three transitional phases including diagnosis, brain metastasis and testis/ovary metastasis, and one absorotion phase of recovery/death have been considered. The distribution was fitted and the probabilities of death or recovery were determined based on the independent variables including age, sex, blood group, etc. Methods: In this modeling study, necessary information was extracted from patients’ medical records (recorded during 2006-2013) available in the Medical Records Department of Afzalipour Hospital of Kerman/ Iran. After excluding the unrelated cases, Phase-type distribution was fitted in which four phases including three transitional phases (cancer diagnosis, brain metastasis, and testis/ ovary metastasis ) and one absorption phase (death or recovery) have been considered. For this purpose, different modeling methods were used for patients who had died and recovered. EM algorithm was used for modeling and fitting Phase-type distribution. Data were analyzed using SPSS22 and R. After fitting Phase-type distribution and determining the probabilities of absorption, the effect of each independent variable on these probabilities was evaluated, and t-test, Pearson’s correlation coefficient, and One-way analysis of variance (ANOVA) were used for the analysis of different variables. Results: The variables of sex and the presence or absence of splenomegaly and hepatomegaly had no effect on the probability of death and recovery. However, the probability of death showed significant relationship (p<0.0001) with the diagnosis of cancer type (ALL or AML) and it was more in patients diagnosed with ALL. Death probability had also significant relationship with brain and testis/ovary metastasis (P=0.002). As expected, the probability of death in patients with brain or testis/ovary metastasis compared to those without matastasis was more. In addition, the p-value of the test used to assess the association between the probability of death and blood groups was 0.025; therefore, there is a significant difference in the probability of death between at least two blood groups. Conclusion: The results show that the diagnosis of cancer type and treatment method can affect the probabilities of death and recovery. Further studies on other variables can help physicians to predict the probabilities of death or recovery during the development of cancer and choose the best treatment method to enhance the probability of recovery in these patients.